41. The equation

d*u P* WL

occurs in finding the shape of a strut which canks a fhrmt «( the cml, *f**l »Uo ft
lateral load. Show that it is satisfied by putting

All the letters except u and JF represent constants.

42. If / = dt sin / + b sin a/ 4- < lin 3/f find the vahir »f ' *in4 ^,

43. If x =s r sin f / + -^ cos 2y/ — ., where * i» the i

df fiftir t of

piston of a steam-engine from the middle of il* »tr*»kr, f • Irngfli of er*ifiJi» / .:. Irn^fh
of connecting rod, find expressions for the vritH-ity ami icrpkr^tlmi,

What are the values of the acceleration when / .-. i?t ami I

2f ' ' f

44. A point motes along a straight line so that if"* ilnf»ttr.«* i fr^m « fi*f»! p»jnl
on the line is given by / -- a sin (2»// »f /*} «f 1 1111 f^w// f ft) ; nt ^ /. ^ «u>:| 4 itr
constants. Write down expressions ft»r the vrlodfy AIP! ar.tr-inrjfifjfi *| tfif Mm**.
Plot a curve to show the Talue of s fc»r any value of / whrn tf : ^ 1*5, 1 ... cifi, 4* **7>J*

/5 = 0*951,7= ?.

113.(DilTerontiation of log M,

If / is a function of a*, and ty and i.r are iiintiltani*ftti't
and 3?) then

nf

This remains true as 9f and «r are Mm

approaches the limiting value '/•

*" rf,r 7T
dy

Let/ • !og4 .
Then ,r /*
,*/i

liliil . . <* sc r
r/r

. ^/F .... f I

r/r i7r r

^

It follows in the same way that

im iiwl »tttattcr9 t